Pre-Calculus  ·  All Units

Trigonometry Master Exam

20 Exam-Style Multiple-Choice Questions  |  Full Solutions Included

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Concept Review & Key Formulas

Unit 1

Angle Measurement & the Unit Circle

Degree ↔ Radian\(\theta_{rad}=\theta_{deg}\cdot\dfrac{\pi}{180}\)
Arc Length\(s = r\theta\)  (\(\theta\) in radians)
Unit CircleRadius = 1; \((\cos\theta,\sin\theta)\)
Coterminal\(\theta \pm 360°\) or \(\theta \pm 2\pi\)

Unit 2

Right-Triangle & General Trig Functions

SOH-CAH-TOA\(\sin=\frac{opp}{hyp},\ \cos=\frac{adj}{hyp},\ \tan=\frac{opp}{adj}\)
Reciprocals\(\csc=\frac{1}{\sin},\ \sec=\frac{1}{\cos},\ \cot=\frac{1}{\tan}\)
Quadrant SignsASTC: All, Sin, Tan, Cos positive
Pythagorean\(\sin^2\theta+\cos^2\theta=1\)

Unit 3

Graphs of Trig Functions

General Form\(y=A\sin(B(x-C))+D\)
Amplitude\(|A|\); Period \(=\dfrac{2\pi}{|B|}\)
Phase Shift\(C\) (right if \(C>0\))
Vertical Shift\(D\) (midline at \(y=D\))

Unit 4

Trigonometric Identities

Sum / Difference\(\sin(A\pm B)=\sin A\cos B\pm\cos A\sin B\)
Double Angle\(\sin 2\theta=2\sin\theta\cos\theta\)
cos Double\(\cos 2\theta=\cos^2\!\theta-\sin^2\!\theta\)
Half Angle\(\sin\frac{\theta}{2}=\pm\sqrt{\frac{1-\cos\theta}{2}}\)

Units 5–6

Inverse Trig, Equations & Laws

Inverse Ranges\(\arcsin:[-\tfrac{\pi}{2},\tfrac{\pi}{2}]\ \ \arccos:[0,\pi]\)
Law of Sines\(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)
Law of Cosines\(c^2=a^2+b^2-2ab\cos C\)
Triangle Area\(\text{Area}=\tfrac{1}{2}ab\sin C\)
Exam Questions

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